Finite Group DatabasebetaFinite Group Databasebeta| order | 8140 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D185 |
| unambiguous semidirect product | (C5×D11)⋊D37 |
| unambiguous semidirect product | (D11×C37)⋊D5 |
| Fitting, socle, derived, Hall | C5×C11×C37 ⋊ C22 |
| Hall | C11×C37 ⋊ C2×D5 |
| Hall | C5×C37 ⋊ C2×D11 |
| Hall | C5×C11 ⋊ C2×D37 |
| Sylow | C37 ⋊ D5×D11 |
| Sylow | C11 ⋊ C2×D185 |
| Sylow | C5 ⋊ D11×D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C11×C37 | C22 |
| LCS | G ▷ C5×C11×C37 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
658 conjugacy classes — view the full character table.
| maximal subgroup of | D11×C5⋊(D37⋊C3), C3×D11×D185, D11×D555, … |
| maximal normal subgroup of | D11×C5⋊(D37⋊C3), C3×D11×D185 |
| maximal quotient of | C3×D11×D185, D11×D555, D33×D185, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8140, 37);